Question: Simplify the expression. $(5t^{4}-4t^{3}-3t^{2})(-t^{2}-5t)$
Solution: First use the distributive property. $ 5 t^4 (- t^2) + 5 t^4 (-5 t) - 4 t^3 (- t^2) - 4 t^3 (-5 t) - 3 t^2 (- t^2) - 3 t^2 (-5 t) $ Simplify. $ - 5t^{6} - 25t^{5} + 4t^{5} + 20t^{4} + 3t^{4} + 15t^{3} $ $-5t^{6}-21t^{5}+23t^{4}+15t^{3}$ Identify like terms. $ {- 5t^{6}} \color{#DF0030} {- 25t^{5}} \color{#DF0030} {+ 4t^{5}} {+ 20t^{4}} {+ 3t^{4}} {+ 15t^{3}} $ Add the coefficients. $ { -5t^{6}} \color{#DF0030} { -21t^{5}} {+ 23t^{4}} {+ 15t^{3}} $